KUK Syllabus 2015

What is Physics? Scope an excitement. Physics in relation to science study and technology.

Physical word & Measurement

Unit for measurement, fundamental and derived units, dimensions, order of magnitude, accuracy and errors in measurement.

Description of Motion in One Dimension

Objects in motion, motion in one dimension. Motion in a straight line, uniform motion, its graphical representation and formulae. General relation between position and velocity, application to uniformly accelerated motion, acceleration in general, one – dimensional motion.

Description of Motion in Two and Three Dimensions

Vectors in two dimensions, general vectors, vectors and scalars, vector addition and multiplication by a real number, zero vector and its properties. Resolution of a vector in a plane, rectangular components. Motion in two dimensions, cases of uniform velocity and uniform acceleration for motion in a plane, uniform circular motion, motion of objects in three – dimensional space.

Laws of Motion

Force and inertia. First law of motion. Second law of motion. Impulse, Kinds of forces in nature. Third law of motion, conservation of momentum, rocket propulsion, equilibrium of concurrent forces. Static and Kinetic friction, laws of friction, rolling friction, lubrication, inertial and non – inertial frames.

Work, Energy and Power

Scalar product of vectors, work done by a constant and a variable force, unit of work, kinetic energy, power. Elastic collisions, Potential energy of a mass. Different forms of energy, mass – energy equivalence, conservation of energy.

Rotational Motion

Inter – dependence of Newton’s law of motion, centre of mass of a rigid body, general motion of a rigid body, nature of rotational motion. Plane ( rotational ) motion of a single particle, torque, angular momentum and its geometrical and physical meaning, conservation of angular momentum, examples of circular motion ( car on a level circular road, car on a banked road ), pendulum, comparison of linear and rotational motions, properties of moment of inertia, parallel axis theorem, examples of two dimensional rigid body motion ( mass point on sting wound on cylinder, cylinder rolling without slipping ).

Gravitation

Acceleration due to gravity, one – dimensional motion under gravity, two dimensional motion under gravity, universal law of gravitation, the gravitational constant, mass of earth, inertia and gravitational mass, variations in the acceleration due to gravity of the earth, geo – stationary satellites, gravitational potential, escape velocity.

Oersted’s observation, Biot – Savart law ( magnetic field due to current element ), magnetic field due to a straight wire, circular loop and solenoid, force on a moving charge in a magnetic field ( Lorentz force ), cyclotron, forces and torques on current in a magnetic field, force between two currents, definition of Ampere, Moving coil galvanometer and conversion into ammeter and voltameter.

Energy changes during a chemical reaction, First law of Thermodynamics ( internal energy, enthalpy, applications of First law of Thermodynamics ), Second law of thermodynamics ( entropy, free energy ), spontaneity of a chemical reaction, free energy change and chemical equilibrium, free energy available for useful work. Third law of Thermodynamics.

Chemical Equilibrium

Law of mass action, chemical equilibrium, effects of changing the conditions of systems of equilibrium, ( change of concentration, pressure and temperature, Lechatelier principle ), ionization of electrolytes, weal and strong electrolytes, various concepts of acids and bases, ionization of water, pH, solubility product, numerical based on these concepts.

Living World, Diversity of Life, Cell and Cell Division, Genetics and Morphology of Plants and Animals.

Physiology of plants, Physiology of animals, Reproduction, Development and Growth, Ecology and Environment and Biology in Human Welfare. OR

KUK 2015 Mathematics Syllabus

Mathematics ( 61 – 90 questions ) – 30 Marks

Sets and Binary Operation

Algebra of sets, Cartesian product of sets, Function, A binary operation defined in Set A as a function from A x A into A. Associatively and commutatively of binary operation. Inverse of an element in A.

Complex Number

Complex number of the form a+ib, representation of complex number in plane, Argand diagram, algebra of complex number, real and imaginary parts of complex number, modulus and argument of complex number, square root of complex number, cube root of unity, triangle inequality.

Quadratic Equations

Solutions of quadratic equation by factorization and formula methods, relation between roots and coefficients, formation of equation symmetric function of roots.

Sequences and Series

Nth term of A.P. sum of N terms of A.P., A.M. between two nos., nth terms of G.P., Sum of n terms of G.P., Sum of infinite terms of G.P., G.M., arithmetic – Geometric series.

Permutations as arrangement, meaning of simple and applications including circular permutation.

Mathematical Induction and Binomiar Theorem

Principal of Mathematical Induction with application, Statement and proof of binomial theorem for positive index. General and particular term of Binomial Theorem for any index. Applications to approximation, properties of Binomial coefficient.

Exponential and Logarithms Series

The infinite series fore : proof that e lies between 2 and 3, Infinite series for log ( 1+x ) and log ( 1+x ) / ( 1 – x ). Calculation of the logarithm of a number using suitable logarithmic series.

Distance formula, section formula, area of triangle, condition of co – linearity, controid, In centre, locus parallel and perpendicular lines, formation of equation of straight lines in different forms. Intersection of two lines, condition for general second degree equation to represent two straight lines.

Circles

Equation of circle, parametric and diametric forms, point of intersection of a line and a circle, condition for a line to be tangent to a circle, equation and length of tangent to a circle form a point. Intersection of two circles, condition that two interesting circles are orthogonal.

Conic Section

Equation of conic section and point of tangency.

Matrices and Determinates

Matrix as a rectangular arrangement of numbers, type of matrices, Quality of matrices, Addition, Scalar multiplication and multiplication of matrices : Linear combination of matrices, non – commutatively and associatively of matrix notations, Determinant, Minors and cofactors of determinant, expansion of a determinant, properties and elementary transformation of determinates. Application of determinants in solution of equations and area of a triangle. Crammer’s rule, Adjoint and inverse of a matrix and its properties, Application of matrices in solving simultaneous equations in three variables.

Vectors and Three Dimensional Geometry

Vector and directed line segment, Magnitude and direction of a vector, Equal vectors. Unit vector, Zero vector. Position vector of a point. Components of a vector, Vector in two and three dimensions, Addition of vectors, Multiplication of a vector by a scalar, Position vector of a point dividing a given straight line in a given ratio, scalar ( dot ) product of the two vectors, cross product of the two vectors, scalar triple product, Applications of vectors in the use of establishment of various geometrical results, Work done=force x displacement, Moment of a force about a point, moment of a couple about a point, Proof of cosine rule. Angle in a semi – circle is a right angle.

Applications of vector product in finding area of a triangle as an area of a parallelogram as. Proof of sine rule. Applications of scalar triple product in finding volume of a parallelepiped, co planarity of vector using scalar triple product. Decomposition of a vector into three non – coplanar directions, as vectors in 3 – D direction ratios and direction cosines for any vector, angle between two vectors where d.c.’s are given.

Distance between two points, condition of the intersection of two lines, shortest distance between two lines, equation of a plane containing a given point and normal to a given direction, angle between two planes, angle between a line a plane. Distance of a point from the plane. Equation of any plane passing through the intersection of the two planes. Equation of a sphere in the form, Equation of sphere with the positions vectors as the extremities of a diameter in the form.

Differential Calculus

Concept of real function, its domain and range, graphs of functions. Composition of functions, meaning of Fundamental theorems of limits. Continuity of a function at a point, over an open / close interval, Properties of continuous function, Continuity of polynomial, trigonometric, exponential, logarithmic and inverse trigonometric functions.

Definition of definite integral as the limit of a sum, fundamental theorem of calculus, evaluation of definite integrals, transformation of definite integrals by substitution, properties of definite integrals, evaluation of some definite integrals using the above properties. Definite integral and area bounded by a curve between two ordinates and x – axis, area between two curves.

Differential Equations

Differential equations, order and degree, formation of a differential equation, general and particular solution of a differential equation, solution of differential equation by the method of Variables Separable, Homogeneous equations and their solution, solution of the liner equation of first order with constant coefficients.

Correlation and Regression

Bi – variable frequency distributions as arising from observation of two variables on the same unit of observation. Marginal and conditional frequency distributions derived from a bi – variable frequency distribution. The concept of relationship between variables introduced as the dependence of conditional distribution on the values of the conditioning variable.

Distinction between relationship and functional relationship. Correlation analysis as the measurement of the strength of relationship between the quantitative variable and regression analysis as the method of predicting the values of one quantitative variable form those of the other quantitative variable. Definition and calculation of the correlation coefficient, positive and negative correlation, perfect correlation.

Use of the scatter diagram in interpreting the values of the correlation coefficient. Calculation of the regression coefficient and the two lines of regression by the method of least square. Use of the lines of regression for prediction, error of prediction and its relation with the coefficient correlation.

Probability

Random experiment and the associated sample space ( i.e. set of all outcomes ), events as subjects of the sample space, occurrence of an event. Sure event, impossible event, mutually exclusive event, elementary event, equally likely elementary events. Definition of probability of an event as the ratio of the number of favourable equally likely events to the total number of equally likely events. Addition rule for mutually exclusive events.

Combination of events through the operations ( and, ‘not’ and their set representation ). Probability of the events ‘A’ or ‘B’ ‘Not A’ conditional probability, Independent events, Independent experiments, Calculation of probabilities of events associated with independent experiments.

Random variable as a function on a sample space ( only randon variable taking finite number of the values be considered ). Distribution of random variable derived from the probabilities of events on the sample space on which the random variable is defined. Binomial Distribution : examples of different random experiments giving rise to random variable with the binomial distribution.